Structure of state-space

Since the CSS may change by adding or splitting off atoms, or due to structure rearrangements of the surface layer under thermal fluctuations (rearrangements 

Let us consider the cluster that comprises m spherical atomic layers surrounding the seeded microcluster. We shall call as adjacent those structure states of two clusters which undergo mutual transformations with the change of the number of atomic layers by unity or (if the transformations are due to the change in the surface layer structure) without this change. 

The line connecting the zero level with any vertex of the subsequent levels is called the line of structure realization or the valley (as adopted in the theory of spin glasses [6.77]). The vertices lying along the valley show the structure states of the microcluster and the cluster core. 

We denote the i-th vertex of the A th level by at(k) (index i numbers the vertices of the same level), and the set of /c-th level vertices (k m + 1) by Mk. The measure of closeness as well as the measure of distinction between two CSS or two cluster core structures can be determined by the position of the point of junction of their valleys. Any two valleys, joining at a level m 1, have a common section. The measure of closeness of two structures (a /c), a2(/c) e Mk) is the number m, and the measure of their distinction is the number 

This relationship defines the metric on the set Mk, transforming the latter into the metric space. It can be easily seen that the metric (6.41) has the property 

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